<![CDATA[Abstract: The research aims to describe the mathematical reasoning of students with Field Dependent (FI) and Field Independent (FD) cognitive style in solving algebra problems. Type of this research is descriptive qualitative. The cognitive styles of 32 students of class VIII H SMPN 2 Karanganyar were determined using Group Embedded Figures Test (GEFT). Each category of cognitive styles was taken three students with the high, medium, and low scores and were used as research subjects. Data was collected by interview based tasks. Validity of the data used time triangulation. Techniques of data analysis were done by: (1) classfying the data into Polyaâs problem solving steps, (2) presenting the data in narrative text, and (3) concluding the studentsâ mathematical reasoning in each Polyaâs problem solving steps. The results of this research showed that mathematical reasoning students with FD cognitive styles in algebra problem solving is: (1) able to identify the problem clearly and completely, (2) able to describe the conditions of the problem, (3) able to connect different elements of information but not perfect. While the mathematical reasoning students with FI cognitive styles in algebra problem solving is: (1) able to identify the problem clearly and completely, (2) able to describe the conditions of the problem, (3) able to connect different elements of information completely, (4) able to apply algebraic concepts that have been studied previously, and (5) able to make conjectures for problem solving strategies but incomplete.Keywords: Mathematical reasoning, algebra problems, cognitive styles]]>
